Random close packing in a granular model

We introduce a two-dimensional lattice model of granular matter. Using a combination of proof and simulation we demonstrate an order/disorder phase transition in the model, to which we associate the granular phenomenon of random close packing. We use Peierls contours to prove that the model is sensitive to boundary conditions at high density and Markov chain Monte Carlo simulation to show it is insensitive at low density. (c) 2010 American Institute of Physics. [doi:10.1063/1.3511359]